Futures Projection Rates and Basis Numbers

Abstract: This paper explores the pricing variables of perpetual and futures contracts within the Talos portfolio management system. For perpetual contracts, we define the contract basis as the relative difference between the contract quote and the index price, introducing a 1-week equivalent rate to simplify basis interpretation. For futures contracts, we introduce the projection rates, defined as the continuously compounded rates used to project the index quote to other maturities. We provide three definitions of projection rates: the forward-starting rate, the zero-maturity rate, and the spot-index rate, each suited for different application contexts. In order to compute the forward prices with the forward-starting projection rates and the zero-maturity projection rates, one also needs to employ the corresponding basis numbers. Similarly, the spot-index projection rates are useful in purely continuous-time models, such as the popular Black-Scholes-Merton model often used to compute option prices. We illustrate these concepts with examples from market data on the Deribit exchange.

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